From quick look at code the likely permissions check for that is edit_comment capability in edit_comment() function.
Your options to remove that capability roughly are:
- customize the role with plugin, for example Members
- customize role with code, probably using remove cap functionality
- filter thiungs around
map_meta_caporuser_has_capif you need to achieve more elaborate logic (for example denying permission in context of specific comment, rather than comments in general)
PS not sure if this will properly omit related parts of interface, might need to deal with that separately
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